The advantage of experience and hindsight is earned only at great cost.
But earn it I did, and so added the right tool (smaller, bottom-bracket specific press), determined the right method (one cup at a time, left first) and purchased the new frame.
This time, I got it right.
Frame: 1070 grams
Cables and housing: 354
Bottom Bracket Cups: 29
Running total: 4189 grams, 9.235164 pounds